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Finite element error analysis of surface Stokes equations in stream function formulation. (English) Zbl 1467.65105

In this paper, an error analysis of a finite element method is presented for the discretization of the coupled system of second order surface PDEs for the stream function, and an auxiliary variable. The PDEs come from a surface Stokes problem in stream function formulation on a simply connected oriented surface in 3D without boundary. As finite element method, the trace finite element method TraceFEM [M. A. Olshanskii and A. Reusken, Lect. Notes Comput. Sci. Eng. 121, 211–258 (2017; Zbl 1448.65245)] is applied and it was proved that the method has optimal order discretization errors for the velocity and pressure. Numerical experiments illustrate relevant properties of the discretization method.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
76D07 Stokes and related (Oseen, etc.) flows
35Q35 PDEs in connection with fluid mechanics

Citations:

Zbl 1448.65245

Software:

Netgen; CutFEM; NGSolve
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

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